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How do you solve the following linear system: # y=2x-1, x-y=5 #?

Answer 1

Isaiah Anthony

The solution for the system of equations is
#color(blue)(x=-4,y=-9#

#color(blue)(y=2x-1#.......equation #(1)#

#x-y=5#.........equation #(2)#

using substitution to solve.

Substituting equation #1# in equation #2#

#x-y=5#

#x-color(blue)((2x-1)=5#

#x-2x +1=5#

#-x +1=5#

#-x =5-1#

#-x =4#

#color(blue)(x =-4#

Finding #y# by substituting #x# in equation #1#:

#color(blue)(y=2x-1#

#y=2*(-4)-1#

#y=-8-1#

#color(blue)(y=-9#

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Answer 2

Kennedy Adams

To solve the linear system ( y = 2x - 1 ) and ( x - y = 5 ):

Substitute the expression for ( y ) from the first equation into the second equation.
This gives ( x - (2x - 1) = 5 ).
Simplify by distributing the negative sign: ( x - 2x + 1 = 5 ).
Combine like terms: ( -x + 1 = 5 ).
Subtract 1 from both sides: ( -x = 4 ).
Divide both sides by -1: ( x = -4 ).
Substitute ( x = -4 ) into the first equation to find ( y ): ( y = 2(-4) - 1 ).
Simplify: ( y = -8 - 1 ).
Compute: ( y = -9 ).
So, the solution to the system is ( x = -4 ) and ( y = -9 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.